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2 years ago

Question 6 of 10 Which choice is equivalent to the product below?

Mathematics

2 answers:

marshall27 [118]2 years ago

8 0

The answer is d because when you get the square root of 8*5 you get 6.32 and when you get the square root of 2 and ten you get the same

ohaa [14]2 years ago

6 0

Answer: D

Step-by-step explanation:

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4. 122 - 4(6) + 1 Evaluate 112 122 - 4(6) + 1 112

san4es73 [151]

Answer:

ans=97

Step-by-step explanation:

(i)u should use BEDMAS RULE.

122-4(6)+1

=122-24+1

=122-25

=97

8 0

2 years ago

If f(x) is a linear function, f(−2)=4, and f(1)=−1, find an equation for f(x)

juin [17]

Answer:

$y = -\frac{5}{3}x+\frac{2}{3}$

Step-by-step explanation:

Given

$f(-2) = 4$

$f(1) = -1$

Required

The equation of the function

The given parameters means that:

$(x_1,y_1) = (-2,4)$

$(x_2,y_2) = (1,-1)$

Calculate the slope (m)

$m = \frac{y_2 -y_1}{x_2 -x_1}$

$m = \frac{-1-4}{1--2}$

$m = \frac{-5}{3}$

The equation is then calculated using:

$y = m(x - x_1) + y_1$

This gives:

$y =\frac{-5}{3}(x--2)+4$

$y =\frac{-5}{3}(x+2)+4$

Open bracket

$y = -\frac{5}{3}x-\frac{10}{3}+4$

Take LCM

$y = -\frac{5}{3}x+\frac{-10+12}{3}$

$y = -\frac{5}{3}x+\frac{2}{3}$

6 0

3 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$